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An a posteriori error control framework for adaptive precision optimization using discontinuous Galerkin finite element method
, 2005
"... Professor Darmofal and the generous funding provided by NASA Langley (grant number NAG103035). Secondly, the effort put into Project X by faculty and students (past and present) have made it possible to carry out the computational demonstrations in higherorder DG. In particular, Krzysztof Fidkowsk ..."
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Cited by 30 (0 self)
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Professor Darmofal and the generous funding provided by NASA Langley (grant number NAG103035). Secondly, the effort put into Project X by faculty and students (past and present) have made it possible to carry out the computational demonstrations in higherorder DG. In particular, Krzysztof Fidkowski and Todd Oliver are to be acknowledged for their contributions towards the development of the flow solvers and also for providing some of the grids for the test cases demonstrated. Finally, thanks must go to thesis committee members Professors Peraire and Willcox as well as thesis readers Dr. Natalia Alexandrov and Dr. Steven Allmaras for the time they put into reading the thesis and providing the valuable feedbacks. 3 46 Adjoint approach to shape sensitivity 117 6.1 Introduction...............................
Review of OutputBased Error Estimation and Mesh Adaptation in Computational Fluid Dynamics
"... Error estimation and control are critical ingredients for improving the reliability of computational simulations. Adjointbased techniques can be used to both estimate the error in chosen solution outputs and to provide local indicators for adaptive refinement. This article reviews recent work on th ..."
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Error estimation and control are critical ingredients for improving the reliability of computational simulations. Adjointbased techniques can be used to both estimate the error in chosen solution outputs and to provide local indicators for adaptive refinement. This article reviews recent work on these techniques for computational fluid dynamics applications in aerospace engineering. The definition of the adjoint as the sensitivity of an output to residual source perturbations is used to derive both the adjoint equation, in fully discrete and variational formulations, and the adjointweighted residual method for error estimation. Assumptions and approximations made in the calculations are discussed. Presentation of the discrete and variational formulations enables a sidebyside comparison of recent work in outputerror estimation using the finite volume method and the finite element method. Techniques for adapting meshes using outputerror indicators are also reviewed. Recent adaptive results from a variety of laminar and Reynoldsaveraged Navier–Stokes applications show the power of outputbased adaptive methods for improving the robustness of computational fluid dynamics computations. However, challenges and areas of additional future research remain, including computable error bounds and robust mesh adaptation mechanics. I.
Approximation of the scattering amplitude and linear systems
 ELECTRON T. NUMER. ANA
, 2008
"... The simultaneous solution of Ax = b and A T y = g, where A is a nonsingular matrix, is required in a number of situations. Darmofal and Lu have proposed a method based on the QuasiMinimal Residual algorithm (QMR). We will introduce a technique for the same purpose based on the LSQR method and sh ..."
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Cited by 6 (0 self)
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The simultaneous solution of Ax = b and A T y = g, where A is a nonsingular matrix, is required in a number of situations. Darmofal and Lu have proposed a method based on the QuasiMinimal Residual algorithm (QMR). We will introduce a technique for the same purpose based on the LSQR method and show how its performance can be improved when using the generalized LSQR method. We further show how preconditioners can be introduced to enhance the speed of convergence and discuss different preconditioners that can be used. The scattering amplitude g T x, a widely used quantity in signal processing for example, has a close connection to the above problem since x represents the solution of the forward problem and g is the righthand side of the adjoint system. We show how this quantity can be efficiently approximated using Gauss quadrature and introduce a blockLanczos process that approximates the scattering amplitude, and which can also be used with preconditioning.
OutputBased Error Estimation and Mesh Adaptation in Computational Fluid Dynamics: Overview and Recent Results
"... Error estimation an control are critical ingredients for improving the reliability of computational simulations. Adjointbased techniques can be used to both estimate the error in chosen solution outputs and to provide local indicators for adaptive refinement. This article reviews recent work on the ..."
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Error estimation an control are critical ingredients for improving the reliability of computational simulations. Adjointbased techniques can be used to both estimate the error in chosen solution outputs and to provide local indicators for adaptive refinement. This article reviews recent work on these techniques for Computational Fluid Dynamics (CFD) applications in aerospace engineering. The definition of the adjoint as the sensitivity of an output to residual source perturbations is used to derive both the adjoint equation, in fullydiscrete and variational formulations, and the adjointweighted residual method for error estimation. Assumptions and approximations made in the calculations are discussed. Presentation of the discrete and variational formulations enables a sidebyside comparison of recent work in output error estimation using the finite volume method and the finite element method. Recent adaptive results from a variety of applications show the power of outputbased adaptive methods for improving the robustness of CFD computations. However, challenges and areas of additional future research remain, including computable error bounds and robust mesh adaptation mechanics. I
Tuned preconditioners for inexact twosided inverse and Rayleigh quotient iteration
, 2013
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Approximation of the scattering amplitude
, 2007
"... The simultaneous solution of Ax = b and A T y = g is required in a number of situations. Darmofal and Lu have proposed a method based on the QuasiMinimal residual algorithm (qmr). We will introduce a technique for the same purpose based on the lsqr method and show how its performance can be improve ..."
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The simultaneous solution of Ax = b and A T y = g is required in a number of situations. Darmofal and Lu have proposed a method based on the QuasiMinimal residual algorithm (qmr). We will introduce a technique for the same purpose based on the lsqr method and show how its performance can be improved when using the Generalized lsqr method. We further show how preconditioners can be introduced to enhance the speed of convergence and discuss different preconditioners that can be used. The scattering amplitude g T x, a widely used quantity in signal processing for example, has a close connection to the above problem since x represents the solution of the forward problem and g is the right hand side of the adjoint system. We show how this quantity can be efficiently approximated using Gauss quadrature and introduce a BlockLanczos process that approximates the scattering amplitude and which can also be used with preconditioners.
APPROXIMATION OF THE SCATTERING AMPLITUDE USING NONSYMMETRIC SADDLE POINT MATRICES by
, 2014
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